Let us call the probability, for a person of age **x** and in
status **j** at time **0**, of being in status **k** at time **t**.
can be obtained by solving the
``forward Kolmogorov equations'', which decompose interval into and .

Introducing the 4 transition forces:

one can write for example:

These 6 differential equations can also be written (8):

with :

Last equations, involving have been suppressed for simplicity. Two of the four equations are redundant, because . The system can therefore clearly be reduced to a set of two first order differential equations involving four forces and submatrix :

Tue Jun 6 00:15:46 DF 1995